Absolutely Continuous Curves in p(X) and the Continuity Equation View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2008

AUTHORS

Luigi Ambrosio , Nicola Gigli , Giuseppe Savaré

ABSTRACT

In this chapter we endow p (X), when X is a separable Hilbert space, with a kind of differential structure, consistent with the metric structure introduced in the previous chapter. Our starting point is the analysis of absolutely continuous curves μ t : (a, b) → p (X) and of their metric derivative |μ′|(t): recall that these concepts depend only on the metric structure of (X), by Definition 1.1.1 and (1.1.3). We show in Theorem 8.3.1 that for p > 1 this class of curves coincides with (distributional, in the duality with smooth cylindrical test functions) solutions of the continuity equation More... »

PAGES

167-200

Book

TITLE

Gradient Flows

ISBN

978-3-7643-8721-1
978-3-7643-8722-8

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-7643-8722-8_10

DOI

http://dx.doi.org/10.1007/978-3-7643-8722-8_10

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1016490043


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